Apparatus and method

ABSTRACT

Apparatus comprising a tool ( 2 ) for forming an aspherical surface on a material ( 14 ), and a support for supporting the material ( 12 ) for rotation about an axis, the arrangement being such that the tool ( 2 ) is restricted to movement with respect to the material ( 14 ) in two substantially linear axes transverse to each other. The apparatus may be a high-performance machine comprising a measuring arrangement ( 18 ) mounted so as to extend substantially across the surface of the material ( 14 ) and serving to measure the distance between the tool ( 2 ) and a referencing region ( 32 ) of the measuring arrangement ( 18 ) which can be in the form of a symmetrical metrology device ( 18 ), the metrology device being structurally unloaded. The apparatus is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.

This invention relates to machine tools, and in particular, grindingmachine tools.

A known use of grinding machine tools is for the production of mirrorsegments needed to produce ground-based telescopes or extra largetelescopes (ELT's). The proposed next generation of ground basedtelescopes or ELT's will bring about an unprecedented demand forhundreds of large off-axis mirror segments each having a diameter in therange of 1 to 2 metres. Such mirror segments will be made from glass orceramic material and have a hexagonal shape as used, for instance, inthe Hobby-Eberly telescope. At present, the manufacturing technologiesfor producing ultra-precise mirrors having a diameter of 1 to 2 metresare associated with processing times of hundreds of hours. Consequently,the time to manufacture hundreds, even thousands, of such mirrors for anELT would involve many years of production.

In the late 1970's, high-precision diamond turning machines were devisedto produce large optics in the 1 to 2 meter diameter range. However,these machines and subsequent machines tend to be of a very large sizeand weight (many tonnes).

According to a first aspect of the present invention, there is providedapparatus comprising a tool for forming an aspherical surface on amaterial, and a support for supporting said material for rotation aboutan axis, the arrangement being such that said tool is restricted tomovement with respect to said material in two substantially linear axestransverse to each other.

According to a second aspect of the present invention, there is provideda method of forming an asphercial surface on a material, comprisingrotating said material about an axis of rotation, moving a tool withrespect to said surface, and restricting the movement of said tool tomovement in two substantially linear axes transverse to each other.

Owing to these two aspects of the invention, it is possible to provide ahigh level of loop stiffness between a tool and the material to beworked.

Advantageously, the two substantially linear axes of tool movement arein a substantially vertical plane in which the rotational axis of thematerial lies.

In this way a machine tool such as a grinding machine or a diamondturning machine can have its tool limited to motions in only two axes,namely substantially vertical movement in a vertical plane andsubstantially horizontal movement in the vertical plane. Thus, theamount of moving parts in the machine is reduced, thereby enabling themachine to be relatively stiff.

Preferably, the loop of stiffness is a substantially quadrangularstiffness loop between the tool and the material.

Having a high level of loop stiffness in a grinding machine is extremelyimportant in grinding ceramics and glasses rapidly whilst maintaininggood form accuracy. In order to ensure that subsequent polishingoperations are effective, the output quality from a fixed abrasivegrinding operation must have both good form accuracy and minimalsub-surface damage, which may be caused by the abrasive grainpenetration depth of the grinding tool. In order to control the abrasivepenetration depth it is necessary to have control of the relative motionof the abrasive surface of the grinding tool with respect to thematerial, or workpiece, surface.

Loop stiffness can be divided into two categories, namely static loopstiffness and dynamic loop stiffness, both of which are, preferably, ata relatively high level. Low levels of static loop stiffness result inedge “roll-off” errors produced when the grinding wheel of the grindingtool moves out of full contact with the workpiece surface. High levelsof dynamic loop stiffness are also critical to permit the control of theabrasive penetration at sufficiently high force levels to provideeffective material removal rates.

An advantage of having a relatively high level of loop stiffness isthat, per unit of time, there is a high output of finished product whichis of good quality.

According to a third aspect of the present invention, there is provideda high-performance machine comprising a tool for working at a surface ofa material, a support which supports said material, and a measuringarrangement mounted so as to extend substantially across said surfaceand serving to measure the distance between said tool and a referencingregion of said measuring arrangement.

Owing to this aspect of the invention, a measuring arrangement can beprovided on a high-performance machine tool for referencing machinemotions against the measuring arrangement.

A high-performance machine tool offers a machining capabilityapproaching a relative accuracy level of 5 parts in one million, i.e. 5microns for a 1 metre workpiece diameter. The measuring arrangementallows the accuracy to be improved to around a relative accuracy levelof 1 part in one million, i.e. 1 micron for a 1 metre workpiece.

Advantageously, the machine tool is a high-performance grinding ordiamond turning machine and the measuring arrangement comprises ametrology frame which has a referencing region in the form of a mirrorand which is mounted on the material support of the machine, and a laserinterferometer system mounted on the high-performance tool.

In this way, the tool, such as a grinding tool or a diamond turningtool, can be moved with great accuracy without a deterioration inperformance.

Preferably, the referencing mirror of the metrology frame is a low-massstraight-edge mirror and the laser interferometer system is a smallindependent laser interferometer mounted on a carriage unit whichcarries the tool. Advantageously, the laser interferometer is mounted onthe upper end of an invar support beam, at the lower end of which thereis an air-bearing linear variable differential transducer (LVDT) contactprobe. Such an arrangement helps to compensate for any errors in thetool motion.

According to a fourth aspect of the present invention, there is providedapparatus comprising a tool for working at a surface of a material, asymmetrical metrology device, and a support upon which said metrologydevice is mounted, said metrology device being structurally unloaded andincluding a single referencing device for providing positionalinformation of said tool with respect to said surface.

Owing to this aspect of the invention, a symmetrical metrology devicewith a single referencing device can be provided on a machine tool andnot have any load bearing parts of the machine attached to it.

Advantageously, the metrology device is a fully symmetrical metrologyframe associated with a laser interferometer system mounted on the toolwhich has only two axes of tool movement.

Thus, a high-accuracy feedback-controlled machine tool can be obtainedin which the position of the tool relative to the material can bemonitored without the need for a multi-axis interferometer system or theneed for the metrology frame to protrude into the working volume.

According to a fifth aspect of the present invention, there is providedapparatus comprising a tool for working at material, said apparatusbeing substantially symmetrical in two substantially vertical planessubstantially perpendicular to and intersecting each other.

Owing to this aspect of the invention, it is possible to provide a fullysymmetrical machine tool which is structurally stable.

Not only is the machine tool symmetrical in a right-to-left directionbut also in a front-to-back direction, which gives the machine tool abox-shape appearance. Such a machine tool is relatively thermally morestable and suffers less from tilt errors caused by thermal gradientswhen the machine is in operation.

According to a sixth aspect of the present invention, there is provideda numerically controlled machine comprising a tool and having twosubstantially linear axes and a rotational axis, a tool surface having apre-determined shape, and a data processing system for generatinggeometric information in relation to said tool surface.

According to a seventh aspect of the present invention, there isprovided a method comprising providing a predetermined shape to asurface of a tool, operating the tool surface against a materialsurface, and generating using a data processing system geometricinformation in relation to the tool surface.

Owing to these two aspects of the invention, it is possible to generategeometric information in relation to change of the shape of the toolsurface.

The tool surface can be an abrasive surface of a grinding tool. Thesurface of the material to be shaped may be non-symmetrical such as thatfor a free-form optical element, such that, during the grindingoperation in which the grinding surface wears in such a manner as todepart from the pre-determined shape, the contact zone between theabrasive surface of the grinding tool and the surface of the materialchanges to tend to produce a non-optimal contact zone. The shape of theabrasive surface is determined by a data processing system such that anychange required or any error to be compensated for can be dealt with.

Advantageously, the data processing system uses Non-Uniform RationalB-Splines (NURBS) to monitor wear of the tool surface.

According to an eighth aspect of the present invention, there isprovided apparatus comprising a tool having a material-contactingsurface, said tool being substantially linearly movable across saidapparatus, a forming device located in the substantially linear path ofsaid tool for forming a desired cross-sectional profile on saidmaterial-contacting surface, a conditioning device having a conditioningsurface for conditioning the formed material-contacting surface, and aninspecting device for determining a cross-sectional profile of saidconditioning surface.

According to a ninth aspect of the present invention, there is provideda method comprising forming with a forming device a desiredcross-sectional profile of a material-contacting surface of a toolarranged to move in a substantially linear path, said forming occurringin said substantially linear path, conditioning said material-contactingsurface by a conditioning surface of a conditioning device, anddetermining with an inspection device the cross-sectional profile ofsaid conditioning surface.

Owing to these two aspects of the invention, it is possible to determinethe cross-sectional profile of the material-contacting surface bydetermining the cross-sectional profile of the conditioning surface.

Advantageously, the forming device is a forming wheel, the conditioningdevice is a dressing stick and the inspecting device is asurface-contacting probe which contacts the conditioning surface of thedressing stick. Preferably, the material-contacting surface is anabrasive surface of a grinding tool having a cup wheel which has asymmetrical toric cross-sectional profile when formed, such that themeasurement of the cross-sectional profile of the conditioning surfacein the one direction can be electronically transposed to givemeasurements in a direction substantially perpendicular to that in whichthe determination is taken. This has the advantage that no movement ofthe tool is needed in the direction perpendicular to that in which thedetermination is taken. This arrangement enables a machine tool whichrequires forming and dressing of a tool surface to have a relativelyhigh degree of stiffness.

In order that the invention can be clearly and completely disclosed,reference will now be made, by way of example, to the following drawingsin which:—

FIG. 1 is a cross-sectional perspective view of a grinding machine,

FIG. 2 is a perspective view from above and one end of the grindingmachine,

FIG. 3 is a cross-section of the grinding machine in a plane atsubstantially a right-angle to that of FIG. 1, and

FIG. 4 is a perspective view from above and the opposite end to that ofFIG. 2.

Referring to FIG. 1, a grinding machine tool 2 comprises a grinding toolpiece 4 which includes a tool spindle portion 6 and a grinding cup wheel8. The machine 2 further comprises two movement sub-systems by way ofwhich the tool 4 is moved and a material-supporting table 12 forsupporting material, or a workpiece 14, to be acted upon by the tool 4.There is a work station 16 at which an operator of the machine 2 cancontrol the machine. The machine 2 also comprises a metrology frame unit18 mounted from a base portion 3 of the machine 2.

In order to minimise the moving masses, the machine motions are limitedto three axes, namely two stacked linear axes which carry the grindingspindle 6 over a single rotary axis of the workpiece 14 supported on thetable 12. A tool carriage unit 10 in which the grinding spindle 6, whichis preferably a hydrostatic oil bearing spindle, is mounted, ispreferably of aluminium construction. The carriage unit 10 is itselffurther mounted on tube-type hydrostatic oil linear bearing rails 20 andmovement of the carriage unit 10 along the rails 20 (i.e. in to and outof the page of FIG. 1) is driven by a pair of linear motors 22 mountedeither side of the hydrostatic bearing rails 20. Two high performancelinear encoders are employed closely positioned to the bearing rails 20.An advantage of this slideway sub-system of the carriage 10 and bearingrails 20 is that the carriage 10 can be removed and replaced with otherslideway tool sub-systems, for example, a diamond turning unit. Movementalong the bearing rails 20 enables the tool 4 to be moved substantiallyhorizontally in a substantially linear path across the workpiece 14 in asubstantially vertical plane of the machine 2, and in relation to athree-dimensional positioning system such movement is in the X-axisdirection. The tool 4 is also movable in a substantially verticaldirection in the substantially vertical plane of the machine 2, which inthe three-dimensional positioning system would be movement in the Z-axisdirection. Movement in the Z-axis is achieved by way of a further pairof motors 22′ (shown also in FIG. 3). To ensure safe operation of theZ-axis, and to reduce motor loading, a double-acting seal-less aircounter-balance cylinder 24 is used in association with Z-axis bearingrails 20′ (see also FIG. 3) and positioned such that it acts close tothe centre of gravity of the moving Z-axis mass. The movement permittedin the Z-axis is much shorter than that permitted in the X-axis. TheZ-axis sub-system forms an integral part of the longer X-axis slidewaysub-system which also includes an X-axis carriage unit 21 in order tominimise any cantilevers. The hydrostatic bearing rails 20 are,preferably, rectangular in cross-section, as shown, and are directlymounted onto the upper portion 23 of the main machine structure. As isthe case with the X-axis sub-system, two linear motors and two encodersare employed using a symmetrical design with minimal parallax errors,i.e. Abbé Offset Error.

The substantially vertical rotary axis of the table 12 which carries theworkpiece 14 is driven by a direct drive hydrostatic oil bearing unit 28which is of a low moving mass. This direct drive hydrostatic oil bearingunit 28 has a small depth to diameter ratio to ensure the distance fromthe motor and an associated rotary encoder to the workpiece surface isminimised.

The grinding spindle 6 is inclined relative to the vertical and is fixedfirmly in position via the carriage unit 10. The grinding wheel 8 istherefore also inclined to the same degree and uses a toric-shaped cupwheel. The cup wheel has an external diameter of approximately 325 mmand provides a grinding speed in the range of 25 to 35 m/s (25 to 35Hz). The combined mass of the tool 4 and the Z-axis sub-system embeddedwithin the X-axis sub-system is minimised to less than 750 Kg.

The whole machine structure is based around a substantially symmetricalbox-shape. It is substantially symmetrical not only from side-to-sidebut also front-to-back and simple shaped castings are used to supportthe main active Z- and X-axis movements. In order to produce a 2 mdiameter free-form optic for a large telescope, the box-shape structureis substantially 3 m in length by substantially 1.5 m in height andwould weigh around 12 tons which is 10% of the total mass of someexisting machines. Obviously, for the production of smaller optics asmaller box-shape structure can be used.

By having the absolute minimum number of active motions of minimal mass,namely the tool being only movable in a single substantially verticalplane of the machine 2, and the use of high stiffness bearings allowsthe machine 2 to have relatively high dynamic and relatively high staticloop stiffness. The loop of stiffness is substantially quadrangular inform with operational forces of the grinding tool 4 being transferredupwardly and outwardly through the periphery of the machine 2 andsubsequently downwardly and inwardly to beneath the workpiece 14. Havingsuch a relatively high degree of static and dynamic loop stiffness, arelatively high output of finished work pieces having good quality canbe achieved.

In having the machine 2 of relatively low mass and of a compact modulardesign, thermal stabilising systems have been incorporated to controlthe temperature of the hydrostatic bearing fluids. Motor cooling systemshave been incorporated for the linear and rotary motors and, inaddition, temperature control of the machine structure itself and thegrinding fluid are also present. High diffusivity materials have beenemployed to reduce the effects of the main slow moving heat sources,i.e. the X-axis motors 22. Furthermore, the top structure 23 of themachine 2 which mounts the X-axis encoders is thermally monitored inorder to independently validate thermal stability. The grating encoderscales which are measuring devices which measure the position on thelinear X- and Z-axes are of low co-efficient of thermal expansion andare suitably restrained to prevent thermal creep. These grating scalesare positioned symmetrically either side of the moving carriages forboth the X- and Z-axes.

Referring to FIG. 2, the metrology frame unit 18 is non-load bearing andis mounted from the base portion 3 of the machine 2 and includes, on anupper substantially horizontal beam 30, a referencing region in the formof a single low mass straight edge mirror 32. Only a single mirror 32need be used owing to the restricted movement of the tool 4 in the Z-and X-axes.

Referring to FIG. 3, the Z-axis carriage unit 10 is provided with anindependent laser interferometer 34 mounted on an upper end of an invarsupport beam 36 which is thermally stable. The laser interferometer 34has a short measurement path in order to minimise ambient effects. Atthe lower end of the invar support beam 36, a first air bearing linearvariable differential transducer (LVDT) probe 38 is present. The laserinterferometer 34 measures the distance to the straight edge mirror 32when the LVDT probe 38 is brought into contact with the surface of theworkpiece 14. The metrology frame unit 18 and the laser interferometer34 therefore provide the ability of in-situ post-process measurement,owing to the measured distance being progressively across the surface ofthe workpiece 14 along the substantially linear path of the X-axismovement and thereby providing a profile of that surface. In a similarway to the structure of the machine 2, the metrology frame unit 18 issubstantially fully symmetrical both from side-to-side and fromfront-to-back.

Referring to FIGS. 3 and 4, after the grinding wheel 8 is fitted ontothe inclined grinding spindle 6, the abrasive surface 40 of the wheel 8needs to be shaped into the correct cross-sectional form which is atoric cross-sectional shape. Therefore, it is necessary to machine thisdesired cross-sectional shape onto the abrasive surface 40. In order toimpart the correct toric cross-sectional shape to the abrasive surface40, the abrasive surface 40 is formed, or trued, against a forming ortruing wheel 42. The truing wheel 42 which has an axis of rotationsubstantially perpendicular to the rotary axis of the workpiece 14 isshaped such that the rim of the wheel, which is preferably of diamondcoated steel, is shaped to have the inverse cross-sectional shape asthat to be imparted to the abrasive surface 40. In order to true thegrinding wheel abrasive surface 40, the tool 4 is moved in the X-axisdirection in the vertical plane to above the rim of the truing wheel 42which is located in a position towards one end of the machine 2, asshown, and lies in the vertical plane through which the tool 4 is moved.After the truing operation, the abrasive surface 40 has the correctcross-sectional shape, but requires a further operation to condition theabrasive surface 40 such that the diamond abrasives thereon protrudebeyond the bond matrix of that surface. This is to ensure that thediamond abrasives cut effectively during the grinding process. Thisconditioning process is conventionally known as dressing and is carriedout by plunging the abrasive surface 40 of the grinding wheel 8 into afixed dressing stick 44 which is located proximally and to one side ofthe truing wheel 42, and is preferably made of an abrasive ceramiccompound. The tool 4 is moved in the X-axis direction after the truingoperation to bring the abrasive surface 40 into contact with the topconditioning surface 46 of the dressing stick 44. Consequently, theconditioning surface 46 is shaped using the abrasive surface 40 of thegrinding wheel 8 which, thus, imparts the cross-sectional shape of theabrasive surface 40 into the conditioning surface 46. Since the dressingstick 44 is located to one side of the truing wheel 42, the truing anddressing operations occur at different positions on the inclinedtoric-shaped abrasive surface. Once the dressing operation has beencompleted, the tool 4 can be used for grinding the surface of thematerial 14. The width of the rim of the truing wheel 42 and the widthof the dressing stick 44 are the same as or greater than the width ofthe abrasive surface 40 of the grinding cup wheel 8.

After grinding for some time, the abrasive surface 40 wears, such thatthe correct toric cross-sectional shape may wear away. However, owing tothe arrangement of the truing wheel 42 and the dressing stick 44 on themachine 2, the machine 2 has a system whereby wear of the abrasivesurface 40 is determined by inspecting the cross-sectional shape of theconditioning surface 46. As is the case with the truing wheel 42, theconditioning surface 46 has a cross-sectional shape which is the inverseof the cross-sectional shape of the abrasive surface 40 and, thus,corresponds to the cross-sectional shape of the truing wheel 42, buttransposed through substantially 90°, which is achieved by the dressingstick 44 being located to one side of the truing wheel 42. Thisinspection system also comprises a second air-bearing contact probe 48,shown in FIG. 3, located on the Z-axis carriage unit 10 on the oppositeside of the carriage unit 10 to the first probe 38.

The dressing stick probe 48 is moved across and contacts theconditioning surface 46 by movement of the tool in the X- and Z-axeswhich results in measurements which give the profile of thecross-sectional shape of the abrasive surface 40. Probing of theconditioning surface 46 occurs only in the X-axis direction along a pathwhich is substantially parallel to the linear path of the tool piece 4.Owing to the symmetrical nature of the abrasive surface 40, themeasurements from the probing of the conditioning surface 46 in theX-axis direction can then be electronically transposed to measure thecross-sectional shape of the abrasive surface 40 in the Y-axis directionindicated by the arrow 50 in FIG. 4. By measuring only in the X-axisdirection, there is no need for the addition of other linear motion axesto the machine 2 which can be expensive and reduces the overallstiffness of the machine 2. In conventional grinding machines, there aretypically four or five motion axes and one of these is dedicated topermit the truing and dressing operations. In the machine 2, there is nodedicated axis for truing nor dressing. Thus, the machine 2 not only hasa relatively high degree of stiffness but it is also of simplerconstruction and is therefore relatively less expensive to produce.Furthermore, the construction of the machine 2 allows it to be ofrelatively low mass.

The relatively low mass of the machine 2 enables an increase in thefrequency of production of good quality finished workpieces 14.

The use of the rotary axis about which the workpiece 14 turns incombination with the linear motion of the tool 4 to define a surface onthe workpiece 14 requires a control system and associated computersoftware to deal with a change in shape of the contact zone between theabrasive surface 40 and the workpiece 14 owing to wearing away of theabrasive surface 40.

Non-Uniform Rational B-Splines, commonly referred as NURBS, have becomethe industry standard for the representation and design, and dataexchange of geometric information processed by computers. NURBS providesa unified mathematical basis for representing both analytic shapes, suchas conic sections and quadric surfaces, as well as free-form entities,such as the surfaces of optical elements. A NURBS curve is defined by

${C(t)} = \frac{\sum\limits_{i = 0}^{n}\; {{N_{i,k}(t)}w_{i}P_{i}}}{\sum\limits_{i = 0}^{n}\; {{N_{i,k}(t)}w_{i}}}$

where k is the order of basis functions, N_(i,k) are the B-spline basisfunctions, P_(i) are control points, and the weight w_(i) of P_(i) isthe last ordinate of the homogeneous point P_(i) ^(w).

One of the key characteristics of NURBS curves is that their shapes aredetermined by the positions of control points. The basis functionsdetermine how strongly control points influence the curve. A series ofpoints, called knots vector, are used in the basis functions topartition the time into non-uniform intervals so that some controlpoints affect the shape of the curve more strongly than others.

With the machine 2 having its toroidal shape grinding wheel, the centerof curvature of the wheel is not in the wheel's rotational axis. Thismakes the tool path over the surface of the workpiece 14 more complex.As already mentioned, the diamond grinding wheel abrasive surface 40will experience a substantial wear in the grinding process. Wear willinduce changes of grind wheel shape and result in significant formerrors on the surface of the workpiece 14, which could be an opticalsurface.

By using a NURBS algorithm, compensation for wheel wear can be provided.The toroidal grinding wheel shape is defined by a NURBS representationwhich has several control points. Changes of wheel shape due to wear ofthe abrasive surface 40 can be modelled by NURBS interpolation which isachieved by adjusting the control points used for defining the toroidalgrinding wheel shape. Therefore the complex shape changes of thegrinding wheel are presented by using relatively little data. Owing tothe wheel shape changes, the tool path across the workpiece 14 will alsobe adjusted by NURBS interpolation to compensate for the grinding wheelwear. The NURBS data will help to maintain the motion smoothness andachieve optical surfaces with high form accuracy.

The advantages of the NURBS grinding wheel wear compensation system arethat NURBS offers a way to represent complex toroidal wheel shapes whilemaintaining mathematical exactness and resolution independence, NURBSgives accurate control over the changes of wheel shapes (the set ofcontrol points and knots which guide the wheel shape, can be directlymanipulated to control its smoothes and curvature), the grinding wheelwear compensation is numerically stable as NURBS curves and surfaces areinvariant under common geometric transformations, such as translation,rotation and perspective projection, and the grinding wheel wearcompensation process is fast as relatively little data is needed torepresent complex wheel shape before and after wear occurs.

The machine 2 is able to grind surfaces of the workpiece 14 such asoptical surfaces to a precision of 1 μm over a 1 m diameter surface, thefinished surfaces having minimal sub-surface damage at depths of 2 to 5μm. This high precision accuracy capability is the result of therelatively high motional repeatability of machine motions throughthermal control, fluid film bearings, machine symmetry, minimisedparallax errors, and error compensation and correction via the in-situmetrology frame unit and its associated post-process measuring system.

Plans for an ELT to be built are in place which has a 100 m diameter andwill need 2000 ultra-precisely machined optical segments of 2 mdiameter. With conventional grinding machines, for the production of therequired free-form optics, each such segment will take around 280 hoursto produce. The machine 2 is capable of producing such segments inaround just 20 hours.

1. Apparatus comprising a tool for forming an aspherical surface on amaterial, and a support for supporting said material for rotation aboutan axis, the arrangement being such that said tool is restricted tomovement with respect to said material in two substantially linear axestransverse to each other.
 2. Apparatus according to claim 1, wherein thetwo substantially linear axes are in a substantially vertical plane inwhich the rotational axis of the material lies.
 3. Apparatus accordingto claim 2, wherein the two substantially linear axes are constituted bya substantially vertical axis of movement in said vertical plane and asubstantially horizontal axis of movement in said vertical plane. 4.Apparatus according to any preceding claim, wherein said apparatus has arelatively high stiffness loop.
 5. Apparatus according to claim 4,wherein the loop of stiffness is a substantially quadrangular stiffnessloop between said tool and said material.
 6. Apparatus according to anypreceding claim, wherein said tool is a grinding machine tool. 7.Apparatus according to claim 6 as appended to claim 4, wherein bothstatic loop stiffness and dynamic loop stiffness are at a relativelyhigh level.
 8. Apparatus according to any preceding claim, and furthercomprising two movement sub-systems by way of which said tool is movedin said two substantially linear axes.
 9. Apparatus according to claim 8as appended to claim 3, wherein a first movement sub-system moves saidtool vertically and a second movement sub-system moves said toolhorizontally.
 10. Apparatus according to claim 8 or 9, wherein the firstmovement sub-system is an integral part of the second movementsub-system.
 11. Apparatus according to any one of claims 8 to 10,wherein the movement sub-systems are removable from said apparatus. 12.Apparatus according to any one of claims 8 to 11, wherein the movementsub-systems comprise respective pairs of associated linear motors andlinear encoders for movement of said tool along respective pairs ofbearing rails.
 13. Apparatus according to any preceding claim whereinsaid tool is a high-performance machine tool further comprising ameasuring arrangement mounted so as to extend substantially across asurface of said material and serving to measure the distance betweensaid tool and a referencing region of said measuring arrangement. 14.Apparatus according to claim 13, wherein said measuring arrangementcomprises a metrology frame including said referencing region, and alaser interferometer system mounted on the high-performance tool. 15.Apparatus according to claim 14, wherein said referencing region is inthe form of a mirror.
 16. Apparatus according to claim 15, wherein saidmirror is a low-mass straight-edge mirror and the laser interferometersystem is a small independent laser interferometer mounted on a carriageunit which carries the tool.
 17. Apparatus according to any one ofclaims 14 to 16, wherein said laser interferometer is mounted on theupper end of an invar support beam, at the lower end of which there isan air-bearing linear variable differential transducer (LVDT) contactprobe.
 18. Apparatus according to any one of claims 14 to 17, whereinsaid metrology frame is a symmetrical metrology frame, and saidapparatus further comprises a support upon which said metrology frame ismounted, said metrology frame being structurally unloaded.
 19. Apparatusaccording to claim 18, wherein said symmetrical metrology frame is afully symmetrical metrology frame.
 20. Apparatus according to any one ofclaims 14 to 19, the arrangement being such that the metrology frame isoutside of the working volume.
 21. Apparatus according to any precedingclaim, wherein said apparatus is substantially symmetrical in twosubstantially vertical planes substantially perpendicular to andintersecting each other.
 22. Apparatus according to claim 21, whereinsaid apparatus is substantially box-shaped.
 23. Apparatus according toany preceding claim, wherein said tool is a numerically controlledmachine tool having a tool surface of a pre-determined shape, and a dataprocessing system for generating geometric information in relation tosaid tool surface.
 24. Apparatus according to claim 23 as appended toclaim 6, wherein said tool surface is an abrasive surface of saidgrinding tool.
 25. Apparatus according to claim 23 or 24, wherein saiddata processing system uses Non-Uniform Rational B-Splines (NURBS) tomonitor wear of said tool surface.
 26. Apparatus according to any one ofclaims 23 to 25, and further comprising a forming device located in oneof said substantially linear axes for forming a desired cross-sectionalprofile on said tool surface, a conditioning device having aconditioning surface for conditioning the formed tool surface, and aninspecting device for determining a cross-sectional profile of saidconditioning surface.
 27. Apparatus according to claim 26, wherein saidforming device is a forming wheel, the conditioning device is a dressingstick and the inspecting device is a surface-contacting probe whichcontacts the conditioning surface of the dressing stick.
 28. Apparatusaccording to claim 26 or 27 wherein said tool comprises a cup wheelwhich includes said surface of said tool and which has a symmetricaltoric cross-sectional profile when formed, such that said measurement ofthe cross-sectional profile of the conditioning surface in one directioncan be electronically transposed to give measurements in a directionsubstantially perpendicular to that in which the determination is taken.29. Apparatus according to any one of claims 8 to 28, wherein thecombined mass of said tool and the two movement sub-systems is less thansubstantially 750 Kg.
 30. Apparatus according to any preceding claim,wherein said material is a free-form optic.
 31. Apparatus according toclaim 30 as appended to claim 22, wherein for a 2 m diameter free-formoptic, the box-shape structure is substantially 3 m in length bysubstantially 1.5 m in height and weighs substantially 12 tons. 32.Apparatus according to any preceding claim, and further comprising athermal stabilising system for controlling the temperature of saidapparatus.
 33. Apparatus according to claim 32, wherein said thermalstabilising system comprises high diffusivity materials.
 34. Apparatusaccording to claim 32 or 33 as appended to claim 12, wherein gratingscales of the encoders are of low co-efficient of thermal expansion andare suitably restrained to prevent thermal creep.
 35. A method offorming an asphercial surface on a material, comprising rotating saidmaterial about an axis of rotation, moving a tool with respect to saidsurface, and restricting the movement of said tool to movement in twosubstantially linear axes transverse to each other.
 36. A methodaccording to claim 35, wherein the two substantially linear axes of toolmovement are in a substantially vertical plane in which the rotationalaxis of the material lies.
 37. A method according to claim 36, whereinthe two substantially linear axes are constituted by a substantiallyvertical axis of movement in said vertical plane and a substantiallyhorizontal axis of movement in said vertical plane.
 38. A methodaccording to any one of claims 35 to 37, wherein said tool is a grindingmachine tool.
 39. A method according to any one of claims 35 to 38,wherein said moving is by way of two movement sub-systems.
 40. A methodaccording to claim 37, 38 or 39, wherein a first movement sub-systemmoves said tool substantially vertically and a second movementsub-system moves said tool substantially horizontally.
 41. A methodaccording to claim 40, wherein the first movement sub-system is anintegral part of the second movement sub-system.
 42. A method accordingto any one of claims 39 to 41, wherein the two movement sub-systems areremovable from said tool.
 43. A method according to any one of claims 35to 42, wherein said tool is a high-performance machine tool and furthercomprising a measuring arrangement mounted so as to extend substantiallyacross a surface of said material and serving to measure the distancebetween said tool and a referencing region of said measuringarrangement.
 44. A method according to any one of claims 35 to 43 andfurther comprising providing a pre-determined shape to a surface of saidtool, operating the tool surface against a surface of said materialsurface, and generating using a data processing system geometricinformation in relation to the tool surface.
 45. A method to claim 44,wherein said data processing system uses Non-Uniform Rational B-Splines(NURBS) for monitoring wear of said tool surface.
 46. A method accordingto claim 44 or 45, and further comprising forming with a forming devicea desired cross-sectional profile of said surface of said tool arrangedto move in one of said substantially linear axes, said forming occurringin one of said substantially linear axes, conditioning said surface ofsaid tool by a conditioning surface of a conditioning device, anddetermining with an inspection device the cross-sectional profile ofsaid conditioning surface.
 47. A method according to claim 46, whereinsaid forming is by a forming wheel, the conditioning is by a dressingstick and the inspecting is by a surface-contacting probe which contactsthe conditioning surface of the dressing stick.
 48. A method accordingto claim 46 or 47, wherein said tool comprises a cup wheel whichincludes said surface of said tool and which has a symmetrical toriccross-sectional profile when formed, such that said measurement of thecross-sectional profile of the conditioning surface in one direction canbe electronically transposed to give measurements in a directionsubstantially perpendicular to that in which the determination is taken.49. A method according to any one of claims 35 to 48, and furthercomprising a thermally stabilising tool.
 50. A high-performance machinecomprising a tool for working at a surface of a material, a supportwhich supports said material, and a measuring arrangement mounted so asto extend substantially across said surface and serving to measure thedistance between said tool and a referencing region of said measuringarrangement.
 51. A machine according to claim 50, wherein said measuringarrangement comprises a metrology frame which includes said referencingregion.
 52. A machine according to claim 51, wherein said referencingregion is in the form of a mirror and said machine further comprises alaser interferometer system mounted on the high-performance tool.
 53. Amachine according to claim 52, wherein said mirror is a low-massstraight-edge mirror and the laser interferometer system is a smallindependent laser interferometer mounted on a carriage unit whichcarries the tool.
 54. A machine according to claim 52 or 53, whereinsaid laser interferometer is mounted on the upper end of an invarsupport beam, at the lower end of which there is an air-bearing linearvariable differential transducer (LVDT) contact probe.
 55. A machineaccording to any one of claims 50 to 54, wherein said measuringarrangement is structurally unloaded.
 56. A machine according to any oneof claims 50 to 55, the machine being substantially symmetrical in twosubstantially vertical planes substantially perpendicular to andintersecting each other.
 57. A machine according to any one of claims 50to 56, wherein said machine is a numerically controlled machine havingtwo substantially linear axes and a rotational axis, a tool surfacehaving a predetermined shape, and a data processing system forgenerating geometric information in relation to said tool surface.
 58. Amachine according to claim 57, the arrangement being such that said toolis restricted to movement with respect to said material in said twosubstantially linear axes.
 59. A machine according to claim 57 or 58,wherein said tool is substantially linearly movable across saidapparatus, and further comprises a forming device located in thesubstantially linear path of said tool for forming a desiredcross-sectional profile on said tool surface, a conditioning devicehaving a conditioning surface for conditioning the formed tool surface,and an inspecting device for determining a cross-sectional profile ofsaid conditioning surface.
 60. Apparatus comprising a tool for workingat a surface of a material, a symmetrical metrology device, and asupport upon which said metrology device is mounted, said metrologydevice being structurally unloaded and including a single referencingdevice for providing positional information of said tool with respect tosaid surface.
 61. Apparatus according to claim 60, wherein saidsymmetrical metrology device is a fully symmetrical metrology frame. 62.Apparatus according to claim 60 or 61, and further comprising a laserinterferometer system mounted on said tool which has only two axes oftool movement.
 63. Apparatus according to claim 62, wherein said twoaxes of tool movement are substantially linear axes transverse to eachother.
 64. Apparatus according to any one of claims 60 to 63, whereinsaid metrology device is outside of the working volume.
 65. Apparatusaccording to any one of claims 60 to 64, said apparatus beingsubstantially symmetrical in two substantially vertical planessubstantially perpendicular to and intersecting each other. 66.Apparatus according to any one of claims 63 to 65, wherein said tool isa numerically controlled tool having said two substantially linear axes,a tool surface having a pre-determined shape, and a data processingsystem for generating geometric information in relation to said toolsurface.
 67. Apparatus according to claim 66, wherein said tool surfaceis an abrasive surface of a grinding tool.
 68. Apparatus according toclaim 66 or 67, wherein said data processing system uses Non-UniformRational B-Splines (NURBS) to monitor wear of said tool surface. 69.Apparatus according to claim 67 or 68, wherein said tool issubstantially linearly movable across said apparatus, and furthercomprises a forming device located in the substantially linear path ofsaid tool for forming a desired cross-sectional profile on said abrasivesurface, a conditioning device having a conditioning surface forconditioning the formed abrasive surface, and an inspecting device fordetermining a cross-sectional profile of said conditioning surface. 70.Apparatus comprising a tool for working at material, said apparatusbeing substantially symmetrical in two substantially vertical planessubstantially perpendicular to and intersecting each other. 71.Apparatus according to claim 70, wherein said apparatus is substantiallybox-shaped.
 72. Apparatus according to claim 70 or 71, wherein said toolis for forming an aspherical surface on said material, and furthercomprising a support for supporting said material for rotation about anaxis, the arrangement being such that said tool is restricted tomovement with respect to said material in two substantially linear axestransverse to each other.
 73. Apparatus according to claim 72, andfurther comprising a measuring arrangement mounted so as to extendsubstantially across said surface and serving to measure the distancebetween said tool and a referencing region of said measuringarrangement.
 74. Apparatus according to claim 73, wherein said measuringarrangement is a symmetrical metrology device, said metrology devicebeing structurally unloaded and including said referencing region forproviding positional information of said tool with respect to saidsurface.
 75. Apparatus according to any one of claims 72 to 74, whereinsaid tool is a numerically controlled tool having said two substantiallylinear axes, a tool surface having a pre-determined shape, and a dataprocessing system for generating geometric information in relation tosaid tool surface.
 76. Apparatus according to claim 75 wherein said toolis linearly movable across said apparatus, and further comprises aforming device located in the substantially linear path of said tool forforming a desired cross-sectional profile on said tool surface, aconditioning device having a conditioning surface for conditioning theformed tool surface, and an inspecting device for determining across-sectional profile of said conditioning surface.
 77. A numericallycontrolled machine comprising a tool and having two substantially linearaxes and a rotational axis, a tool surface having a predetermined shape,and a data processing system for generating geometric information inrelation to said tool surface.
 78. A machine according to claim 77,wherein said tool surface is an abrasive surface of a grinding tool. 79.A machine according to claim 77 or 78, wherein said data processingsystem uses Non-Uniform Rational B-Splines (NURBS) to monitor wear ofsaid tool surface.
 80. A machine according to any one of claims 77 to79, wherein said tool is for forming an aspherical surface on amaterial, and further comprises a support for supporting said materialfor rotation about an axis, the arrangement being such that said tool isrestricted to movement with respect to said material in said twosubstantially linear axes which are transverse to each other.
 81. Amachine according to claim 80, and further comprising a measuringarrangement mounted so as to extend substantially across the surface ofsaid material and serving to measure the distance between said tool anda referencing region of said measuring arrangement.
 82. A machineaccording to any one of claims 77 to 81, wherein said numericallycontrolled machine is a high-performance numerically controlled machine.83. A machine according to claim 81 or 82, wherein said measuringarrangement comprises a symmetrical metrology device, and a support uponwhich said metrology device is mounted, said metrology device beingstructurally unloaded and including said referencing region forproviding positional information of said tool with respect to thesurface of said material.
 84. A machine according to any one of claims77 to 83, wherein said machine is substantially symmetrical in twosubstantially vertical planes substantially perpendicular to andintersecting each other.
 85. A machine according to any one of claims 77to 84, said tool being substantially linearly movable across saidapparatus, and further comprising a forming device located in thesubstantially linear path of said tool for forming a desiredcross-sectional profile on said tool surface, a conditioning devicehaving a conditioning surface for conditioning the tool surface, and aninspecting device for determining a cross-sectional profile of saidconditioning surface.
 86. A method comprising providing a pre-determinedshape to a surface of a tool, operating the tool surface against amaterial surface, and generating using a data processing systemgeometric information in relation to the tool surface.
 87. A methodaccording to claim 86, wherein said data processing system usesNon-Uniform Rational B-Splines (NURBS) for monitoring wear of said toolsurface.
 88. A method according to claim 86 or 87, and furthercomprising forming an asphercial surface on said material surface, saidaspherical spherical surface formed by rotating the material about anaxis of rotation, moving said tool with respect to said surface, andrestricting the movement of said tool to movement in two substantiallylinear axes transverse to each other.
 89. A method according to any oneof claims 86 to 88, and further comprising forming with a forming devicea desired cross-sectional profile of the tool surface, the tool beingarranged to move in a substantially linear path, said forming occurringin said substantially linear path, conditioning the tool surface by aconditioning surface of a conditioning device, and determining with aninspection device the cross-sectional profile of said conditioningsurface.
 90. Apparatus comprising a tool having a material-contactingsurface, said tool being substantially linearly movable across saidapparatus, a forming device located in the substantially linear path ofsaid tool for forming a desired cross-sectional profile on saidmaterial-contacting surface, a conditioning device having a conditioningsurface for conditioning the formed material-contacting surface, and aninspecting device for determining a cross-sectional profile of saidconditioning surface.
 91. Apparatus according to claim 90, wherein saidforming device is a forming wheel, the conditioning device is a dressingstick and the inspecting device is a surface-contacting probe whichcontacts the conditioning surface of the dressing stick.
 92. Apparatusaccording to claim 90 or 91, wherein said material-contacting surface isan abrasive surface of a grinding tool having a cup wheel which has asymmetrical toric cross-sectional profile when formed.
 93. Apparatusaccording to any one of claims 90 to 92, wherein said determining of thecross-sectional profile of the conditioning surface in one direction canbe electronically transposed to give measurements in a directionsubstantially perpendicular to that in which the determination is taken.94. Apparatus according to claim 92 or 93, wherein said grinding tool isfor forming an aspherical surface on a material, and further comprises asupport for supporting said material for rotation about an axis, thearrangement being such that said grinding tool is restricted to movementwith respect to said material in two substantially linear axestransverse to each other.
 95. Apparatus according to claim 94, andfurther comprising a measuring arrangement mounted so as to extendsubstantially across said material and serving to measure the distancebetween said grinding tool and a referencing region of said measuringarrangement.
 96. Apparatus according to any one of claims 92 to 95,wherein said grinding tool is a high-performance grinding tool. 97.Apparatus according to claim 95 or 96, wherein said measuringarrangement comprises a symmetrical metrology device, and a support uponwhich said metrology device is mounted, said metrology device beingstructurally unloaded and including said referencing region forproviding positional information of said grinding tool with respect tothe material surface.
 98. Apparatus according to any one of claims 90 to97, wherein said apparatus is substantially symmetrical in twosubstantially vertical planes substantially perpendicular to andintersecting each other.
 99. Apparatus according to any one of claims 90to 98, wherein said tool is a numerically controlled tool, saidmaterial-contacting surface having a predetermined shape, and a dataprocessing system for generating geometric information in relation tosaid material-contacting surface.
 100. Apparatus according to claim 99,wherein said data processing system uses Non-Uniform Rational B-Splines(NURBS) to monitor wear of said material-contacting surface.
 101. Amethod comprising forming with a forming device a desiredcross-sectional profile of a material-contacting surface of a toolarranged to move in a substantially linear path, said forming occurringin said substantially linear path, conditioning said material-contactingsurface by a conditioning surface of a conditioning device, anddetermining with an inspection device the cross-sectional profile ofsaid conditioning surface.
 102. Apparatus according to claim 101,wherein said tool is a grinding tool having a cup wheel which has asymmetrical toric cross-sectional profile when formed, said methodfurther comprising electronically transposing the determination of thecross-sectional profile of the conditioning surface taken in onedirection to give measurements in a direction substantiallyperpendicular to that in which the determination is taken.
 103. A methodaccording to claim 101 or 102, and further comprising forming anasphercial surface on a material, including rotating said material aboutan axis of rotation, moving said tool with respect to said surface, andrestricting the movement of said tool to movement in two substantiallylinear axes transverse to each other.
 104. A method according to any oneof claims 101 to 103, and further comprising providing a pre-determinedshape to said material-contacting surface, operating saidmaterial-contacting surface against the material surface, and generatingusing a data processing system geometric information in relation to thetool surface.
 105. A method according to claim 104, wherein said dataprocessing system uses Non-Uniform Rational B-Splines (NURBS) formonitoring wear of said material-contacting surface.